A rectangle and a triangle below have the same height and base measurements. Find the area of the rectangle and the right triangle, and then compare the areas
The area of rectangle is ____ square inches. The area of the triangle is __ square inches . The area of the triangle is ___ the area of the rectangle
Answers
The area of the rectangle is 48 in².
The area of the triangle is 24 in².
The area of the triangle is half the area of the rectangle.
How to calculate the area of a rectangle and a triangle?To calculate the area of a rectangle, we multiply the length of the rectangle by its width. And to calculate the area of a triangle we multiply the base of the triangle to the height of the triangle and divide by 2.
To calculate the area of the rectangle, we use the formula below
Formula:
A = LW....................... Equation 1Where:
A = Area of the rectangleL = Length of the rectangleW = Width of the rectangleFrom the question,
Given:
L = 6 inW = 8 inSubstitute into equation 1
A = 6×8A = 48 in²Also, the area of the triangle is given by the formula below
A' = bh/2.................. Equation 2Where:
A' = Area of the triangleb = Base of the triangle = 6 inh = Height of the triangle = 8 inSubstitute into equation 2
A' = (6×8)/2A' = 24 in²Hence, the area of the triangle is half the area of the rectangle.
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Related Questions
Find the equation of the line shown ?
Answers
Answer:
y=2x+3
Step-by-step explanation:
find x
look for points (2,7), (3,9), (0,3)
(x2-x1), (y2-y1)
x - distance from 7 and 9: (9-7=2)
y - distance from 2 and 3: (3-2=1)
Rise(y) over run (x) = 2/1=2
so X=2
y=2x
Because we see the line passes the point (0,3) we know the b in y=mx+b = 3
To prove:
try a point
(2,7)
y=mx+b (plug-in)
7=2(x)+3 (isolate x, subtract 3 to 7)
4= 2x (isolate x, divide by 2)
x=2
2=2 ( compare x to original coordinate: (2,7))
Solve for X. Round to the nearest tenth
Answers
Answer:
x=7.9*tan(54°)=10.87
The graph shows a line of best fit for data collected on the number of students enrolled at a university as a function of the number of faculty employed there. Which equation represents the line of best fit? A. y= 20x B. y=1/50 C. y=2x D. y=x
Answers
The equation that represents the line of best fit is given as follows:
y = 50x.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.From the graph, when x = 0, y = 0, hence the intercept b is given as follows:
b = 0.
When x = 10, y = 500, hence the slope m is given as follows:
m = 500/10
m = 50.
Hence the equation is given as follows:
y = 50x.
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Check these questions?
Answers
Answer: Looks pretty good :) !
Question 22 of 30
What is the y-intercept of the line y=1/2x-5?
O A. - 1/2
OB. 5
O C.1/2
OD. -5
Answers
Answer:
-5
Step-by-step explanation:
if u graph it, you can see where the y-intercept is.
What is the surface area of the cylinder below? use pi
Answers
The surface area will be equal to 1,017.9 square feet.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
Given that:-
The given radius is 9 feet.The height of the cylinder is 18 feet.The surface area of the cylinder will be calculated as:-
SA = 2 πrl
SA = 2 π x 9 x 18
SA = 1,017.9 square feet
Therefore surface area will be equal to 1,017.9 square feet.
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The surface area of the given cylinder is 486π m² or 1526m².
From the figure, given height of the cylinder (h) = 18m
Given radius of the cylinder (r) = 9m
To find out the surface area of the cylinder the formula s = 2πr² + 2πrh
By substituting the given radius and height of the cylinder in the above equation we get the required surface area value.
s = 2πr² + 2πrh
s = (2 x π x (9)²) + (2 x π x 9 x 18)
s = (2 x π x 81) + (324π)
s = 162π + 324π
s = 486π m²
s = 486 x 3.14...... (since, π = 3.14....)
s = 1526m²
From the above explanation, we can conclude that the surface area of the given cylinder is equal to 486π m² or 1526m².
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PLEASE HELP I'LL GIVE THE BRAINLIEST!
Answers
Answer:
Box A: 2 × 4.5 × 6 = 54 cubic inches
Box B: 6 × 2.5 × 3 = 45 cubic inches
Box C: 5 × 4.5 × 2.25 =
50.625 cubic inches
Box D: 2.5 × 2.25 × 3 = 16.875 cubic inches
From least to greatest, the order of the boxes' volumes is D, B, C, A.
For the right triangles below, find the exact values of the side lengths b and a. If necessary, write your responses in simplified radical form.
30°
2
Ъ
=
45°
a =
60°
8
Answers
The sides of the triangle are;
c = 5√2
b = 3√3
What is the right triangle?A right triangle is a triangle that has a right angle that measures 90 degrees. The hypotenuse, which is the side that faces the right angle, is the longest side. The right triangle's other two sides are referred to as its legs.
1) Cos 45 = 5/c
√2/2 = 5/c
c√2 = 10
c = 10/√2
c = 5√2
2) Tan 30 = b/3
√3/3 = b/3
3√3= 3b
b = 3√3/3
b = 3√3
We have used to concept of the special angles to solve the problem above.
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Find the area of the parallelogram.
Answers
Answer: 252cm^2
Step-by-step explanation:
Find height of parallelogram using the triangle.
[tex]a^2+b^2=c^2\\(9)^2+b^2=(15)^2\\b^2=114\\b=12[/tex]
Now that we have the height, we can fnd the area of the parallelogram using A=bh.
A = (12)(21)
A =252cm^2
Solve for x: 6x1/4(4x+8)>12
Answers
1. Simplify both sides by dividing both sides by 6: x^(1/4)(4x + 8) > 2
2. Distribute x^(1/4) into (4x + 8): 4x^(5/4) + 8x^(1/4) > 2
3. Simplify by subtracting 2 from both sides: 4x^(5/4) + 8x^(1/4) - 2 > 0
4. Factor out 2 from the left side: 2(2x^(5/4) + 4x^(1/4) - 1) > 0
5. Divide both sides by 2: 2x^(5/4) + 4x^(1/4) - 1 > 0
We can use a sign table to solve this inequality:
| x^(1/4) | x^(5/4) | 2x^(5/4) | 4x^(1/4) - 1 | 2x^(5/4) + 4x^(1/4) - 1 |
|---------|---------|-----------|--------------|---------------------------|
| 0 | 0 | 0 | -1 | -1 |
| 1 | 1 | 2 | 3 | 5 |
From the table, we can see that the expression 2x^(5/4) + 4x^(1/4) - 1 is greater than 0 when x is either less than 0 or greater than 1. Therefore, the solution to the inequality 6x^(1/4)(4x + 8) > 12 is x < 0 or x > 1.
6x^(1/4)(4x+8) > 12
Divide both sides by 6:
x^(1/4)(4x+8) > 2
Divide both sides by 4:
x^(1/4)(x+2) > 1/2
Raise both sides to the 4th power:
x(x+2)^4 > 1/16
Expand the left side:
x(x^4 + 8x^3 + 24x^2 + 32x + 16) > 1/16
Simplify:
x^5 + 8x^4 + 24x^3 + 32x^2 + 16x - 1/16 > 0
This is a fifth-degree polynomial inequality, which can be difficult to solve algebraically. However, we can use numerical methods or a graphing calculator to find the solution.
One possible solution is x > -0.3. We can check this by plugging in a value slightly larger than -0.3, such as x = -0.2:
x^(1/4)(x+2) = (-0.2)^(1/4)(-0.2+2) ≈ 0.83
This is greater than 1/2, so the inequality holds for x = -0.2.
Therefore, the solution to the inequality is x > -0.3.
Prediction Equations ~ questions a and b
Answers
Hence, Equation of line is y= -17 x+420 and Predict the number of fan clubs in the U.S. in 2012 is -33784.
what is the slope?
The slope of a line is its vertical change divided by its horizontal change, also known as rise over run. When you have 2 points on a line on a graph the slope is the change in y divided by the change in x.
What is a prediction ?The process of predicting inside of the observed x values observed in the data is called interpolation. The process of predicting outside of the observed x values observed in the data is called extrapolation.
according to question,
[tex](x_1,y_1)=(4,348) \\and (x_2,y_2)=(6,314)\\[/tex]
and y-intercept point=c=420
slope
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{314-348}{6-4}\\m=\frac{-34}{2}\\m= -17[/tex]
(a).now,equation of line ,y=mx+c
⇒y= -17x+420..(i)
(b). for 2012,x=2012
now value of x is substitute in (i),
⇒y= -(17*2012)+420
⇒y = -34204+420
⇒y= -33784.
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in the previous example, the standard deviation of birth weights for individual babies in the population is 500 grams. what is the standard deviation of the mean birth weights for samples of 100 babies?
Answers
The standard deviation of the mean birth weights for samples of 100 babies is 50 grams.
The standard deviation of the mean birth weights for samples of 100 babies can be calculated using the formula:
Standard deviation of the mean = Standard deviation of the population / sqrt(sample size)
Given that the standard deviation of birth weights for individual babies in the population is 500 grams, and the sample size is 100, we can plug in these values into the formula:
Standard deviation of the mean = 500 / sqrt(100) = 50 grams
Therefore, the standard deviation of the mean birth weights for samples of 100 babies is 50 grams.
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A boutique sells blouses and purses. The blouses cost $28 each and the purses cost $39 each. On a certain day the store sells three times as many blouses as purses. If the store sold $1107 worth of these two items on that day, how many of each were sold
Answers
Thus, the store sold 9 purses and 27 blouses on that day, and the total revenue from selling these items was $1107.
To solve this problem, we need to use algebraic equations. Let's start by assigning variables to the unknown quantities. Let x be the number of purses sold and y be the number of blouses sold.
From the problem, we know that the blouses cost $28 each and the purses cost $39 each. Therefore, the total revenue from selling x purses and y blouses is given by:
Revenue = 28y + 39x
We also know that the store sold three times as many blouses as purses. Therefore, we can write:
y = 3x
Now we can substitute y = 3x into the revenue equation and solve for x:
1107 = 28y + 39x
1107 = 28(3x) + 39x
1107 = 84x + 39x
1107 = 123x
x = 9
So the store sold 9 purses. To find the number of blouses, we can use the equation y = 3x:
y = 3x = 3(9) = 27
Therefore, the store sold 27 blouses.
In summary, the store sold 9 purses and 27 blouses on that day, and the total revenue from selling these items was $1107.
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if a building is 130 feet tall and is viewed from a spot on the ground 80 feet away from the base of the building, what is the slope of a line from the spot on the ground to the top of the building? (round your answer to two decimal places.)
Answers
Answer:
The slope of that line is 13/8 = 1.625
(1.63 to two decimal places).
The triangle above has the following measures
m/C=45 degrees
a=7.5 yd
Use the 45-45-90 Trangle Theorem to find the
length of the hypotenuse Include correct units.
Show all your work.
Answers
The length of the hypotenuse is given as follows:
b = 10.6 yd.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.By the 45-45-90 Triangle Theorem, the two sides have the same length, hence:
a = c = 7.5.
Hence the hypotenuse b is obtained as follows:
b² = a² + c²
b² = 7.5² + 7.5²
[tex]b = \sqrt{7.5^2 + 7.5^2}[/tex]
b = 10.6 yd.
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PLSSSSSSSSSSSSSSS HELP I WILL MARK GOOD ANSWERS BRAINLYEST FOOL ANSWERS WILL GET REPORTED
Answers
because kailey flipped heads 15 times out of 20 coin flips, i think this is 15/20 simplified to 3/5. this is 0.6 and 60%.
olivia flipped tails 9 times out of 20 so it’s 9/20 i think. it’s also 0.45 and 45%.
im so sorry if im wrong btw
Answer:
Kailey flipping heads: 3/4 as a fraction, 0.75 as a decimal, and 75% as a percent.
Olivia flipping tails: 9/20 as a fraction, 0.45 as a decimal, and 45% as a percent.
Step-by-step explanation:
Kailey flipped heads 15 times and tails 5 times.
First, find the total amount of times that Kailey flipped the coin.
15+5=20
Kailey flipped the coin 20 times.
Out of those 20 times, she flipped heads 15 times. We can rewrite this as:
[tex]\frac{15}{20}[/tex]
and simplify it:
[tex]\frac{3}{4}[/tex]
3/4 as a decimal is 0.75, and to find the percentage, simply multiply the decimal form by 100.
We can find that 3/4 as a percentage is 75%.
So, the probability of Kailey flipping heads is:
3/4 as a fraction, 0.75 as a decimal, and 75% as a percent.
Olivia flipped heads 11 times and tails 9 times.
Let's find how many times she flipped the coin.
11+9=20
Olivia flipped the coin 20 times.
Out of 20 times, Olivia flipped tails 9 times.
This can be rewritten as:
[tex]\frac{9}{20}[/tex]
This fraction is already in simplest form.
To find what 9/20 is as a decimal, divide 9 by 20. You'll get 0.45.
Now, multiply 0.45 by 100 to find the percent. You'll get 45%.
So, the probability of Olivia flipping tails is:
9/20 as a fraction, 0.45 as a decimal, and 45% as a percent.
10. In the first circle below write the last letter of the first word beginning with "L".
00000
11. Cross out the number necessary, when making the number below one million.
10000000000
12. Draw a line from circle 2 to circle 5 that will pass below circle 2 and above circle 4.
00000
13. In the line below cross out each number that is more than 20 but less than 30.
31 16 48 29 53 47 22 37 98 26 20 25
Answers
The final answers are given below
[tex]10.[/tex]L
[tex]11.[/tex] [tex]3[/tex] (the number should be [tex]1,000,000[/tex], which has six zeros)
[tex]00000[/tex]
[tex]12[/tex] | |
[tex]00000[/tex]
|
[tex]00000[/tex]
[tex]15. 31 16 48 29 53 47 22 37 98 26 2025[/tex]
What do you mean by number?A number is an arithmetic value that is used to calculate and represent a quantity.
The numbers that are more than [tex]20[/tex] but less than [tex]30[/tex] are [tex]22[/tex] and [tex]26[/tex], so they should be crossed out:
[tex]31 16 48 29 53 47[/tex] X [tex]37 98[/tex] X [tex]2025[/tex]
Therefore the answers are given below.
[tex]10.[/tex]L
[tex]11.[/tex] [tex]3[/tex] (the number should be [tex]1,000,000[/tex], which has six zeros)
[tex]00000[/tex]
[tex]12[/tex] | |
[tex]00000[/tex]
|
[tex]00000[/tex]
[tex]15. 31 16 48 29 53 47 22 37 98 26 2025[/tex]
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What is an equation of the line that passes through the points (6,4) and (-5,4)?
Answers
Hello and Greetings Brainly users.
Answer:The equation of the line that passes through the points (6,4) and (-5,4) is y = 4 , since it is a horizontal straight line through the values of y = 4.Step-by-step explanation:This is an exercise in "Equation of the line that passes through two points". The equation of a line is a mathematical formula used to describe a straight line in a Cartesian plane.
To find the equation of a line that passes through two points, you must first calculate the slope using the formula: m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the given points. Then, the point-slope form of the equation of the line is used to obtain the equation of the line: y - y₁ = m(x - x₁).
By solving this equation, we can obtain the equation of the line that passes through two points. If the slope of the line is zero, as in the case of two points lying on the same horizontal line, then the equation of the line is simply a horizontal line at y = k, where k is the y-coordinate of the points.
As it tells us, we first need to calculate the slope of the line.Applying the following formula:
m = (y₂ - y₁) / (x₂ - x₁)
where m is the slope of the line.
We find that the points are:
x₁ = 6 , y₁ = 4
x₂ = -5 , y₂ = 4
We substitute the data in the formula and solve:
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - 4)/(-5-6)
m = 0/-11
m = 0
Now, we can use the point-slope form of the equation of the line to obtain the equation of the line:
y - y₁ = m(x - x₁)Where m = 0 and (x₁, y₁) is one of the two given points. We can choose any of the two points, but for this we will choose (6,4).
So, substituting the values we have, we have:
y - 4 = 0(x - 6)
Simplifying, we arrive at:
y - 4 = 0
y = 4
The equation of the line that passes through the points (6,4) and (-5,4) is y = 4 , since it is a horizontal straight line through the values of y = 4.
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DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!! 20 POINTS
Students in a high school mathematics class decided that their term project would be a study of the strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as “strict”. They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students.
1. Describe the parameter of interest and a statistic the students could use to estimate the parameter.
2. Is the best design for this study a sample survey, an experiment, or an observational study? Explain your reasoning.
3. The students quickly realized that, as there is no definition of “strict”, they could not simply ask a student, “Are your parents or guardians strict?” Write three questions that could provide objective data related to strictness.
4. Describe an appropriate method for obtaining a sample of 100 students, based on your answer in question 1.
Answers
Answer:
1. The parameter of interest is the proportion of students in the school who think of their parents or guardians as “strict”. A statistic that the students could use to estimate the parameter is the proportion of students in their sample who think of their parents or guardians as “strict”.
2. The best design for this study is a sample survey. An experiment would involve manipulating the parents' behavior and observing the effect on the students, which is not ethical. An observational study would only observe the behavior without manipulation, but it is not clear what behavior to observe in this case.
3. Here are three questions that could provide objective data related to strictness:
How often are your parents or guardians late to pick you up from school or activities? How often do your parents or guardians check your homework or schoolwork? How often do your parents or guardians allow you to go out with friends on school nights?4. An appropriate method for obtaining a sample of 100 students is random sampling. The students could assign each student in the school a number, and then use a random number generator to select 100 numbers. They could then survey the students corresponding to those numbers. Another method could be stratified sampling, where the students divide the school into groups based on grade level, and then randomly sample a proportionate number of students from each group.
Could
7.7
cm
,
4.0
cm
,
7.7 cm,4.0 cm,7, point, 7, start text, space, c, m, end text, comma, 4, point, 0, start text, space, c, m, end text, comma and
1.7
cm
1.7 cm1, point, 7, start text, space, c, m, end text be the side lengths of a triangle?
Choose 1 answer:
yes
or
no?
Answers
By triangle inequality theorem 7.7 cm,4.0 cm, 1.7 cm can not sides of the triangle.
We know that the triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
For example, is a, b and c be sides of triangle then a + b ≥ c.
Here, the sides of triangle are: 7.7 cm, 4.0 cm, 1.7 cm
Let a = 7.7 cm,
b = 4.0 cm,
c = 1.7 cm
consider the sum of sides b and c.
b + c = 4. 0 + 1.7
b + c = 5.7 cm
which is not greater than 7.7 cm (length of side 'a')
This means that, by triangle inequality theorem 7.7 cm,4.0 cm, 1.7 cm can not sides of the triangle.
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The complete question is:
Could 7.7 cm,4.0 cm, 1.7 cm be the side lengths of a triangle?
What is 6×28. Please show me a picture. This is my homework. My teacher requires a picture for my homework and I love that stuff and it would really help me out. Thanks.
Answers
Answer: Im sorry i dont have a picture :( but the awnser to your problem is (168)
Step-by-step explanation:
the primary condition for which a patient is receiving care is communicated to the third-party payer through a(n) __________ code on the healthcare claim
Answers
The primary condition for which a patient is receiving care is communicated to the third-party payer through a diagnosis code on the healthcare claim.
The diagnosis code is a standardized code that represents the patient's medical condition or illness as determined by the healthcare provider. These codes are typically based on the International Classification of Diseases (ICD) coding system, which is used worldwide for reporting diagnoses and medical procedures.
By including the appropriate diagnosis code on the healthcare claim, healthcare providers can communicate to third-party payers the reason for the services or procedures provided. This information is essential for processing and reimbursing healthcare claims accurately and efficiently.
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The primary condition for which a patient is receiving care is communicated to the third-party payer through a(n) ICD (International Classification of Diseases) code on the healthcare claim.
The ICD code serves as a standardized system for classifying diseases and health conditions, enabling clear
communication between healthcare providers and third-party payers.
The primary condition for which a patient is receiving care is communicated to the third-party payer through a
diagnosis code on the healthcare claim. Diagnosis codes, also known as ICD codes (International Classification of
Diseases codes), are standardized codes that represent the specific medical condition or disease being treated by the
healthcare provider.
These codes are used to ensure accurate and timely payment for services rendered and to track healthcare utilization
and outcomes.
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5,5,6,9,4,3,4,8,10,4 what is the range
Answers
Answer: Symbol max-min and answer 10-4
Step-by-step explanation:
Explain how to plot the point (3, -7) on the coordinate plane.
Answers
Answer:
Starting at the origin (0, 0), go right 3 units, then down 7 units. You will end at (3, -7).
please answer correctly
Answers
The location of point P within line segment AB is (8.333, - 6.667).
How to find the coordinates of a point within a line segment
Herein we find the a line segment whose endpoints are A(x, y) = (10.2, - 6) and B(x, y) = (4.6, - 8), in which we must locate the point P. This can be done by following line segment AB:
P(x, y) = A(x, y) + (2 / 6) · [B(x, y) - A(x, y)]
P(x, y) = (10.2, - 6) + (2 / 6) · [(4.6, - 8) - (10.2, - 6)]
P(x, y) = (10.2, - 6) + (1 / 3) · (- 5.6, - 2)
P(x, y) = (10.2, - 6) + (- 1.867, - 0.667)
P(x, y) = (8.333, - 6.667)
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Are 90 degrees (clockwise) and -270 degrees (counter clockwise) coterminal? WHY or why not?
Answers
Yes, 90 degrees (clockwise) and -270 degrees (counterclockwise) are coterminal angles.
What are coterminal angles ?Two angles are coterminal if they share the same terminal side when drawn in standard position. In other words, coterminal angles differ by an integer multiple of 360 degrees.
To see if 90 degrees and -270 degrees are coterminal, we can add 360 degrees to the smaller angle (-270 degrees) and see if we get the other angle:
-270 + 360 = 90
Since we obtain 90 degrees after adding 360 degrees to -270 degrees, these two angles are coterminal. They share the same terminal side in standard position, even though their rotations have different directions (clockwise and counterclockwise).
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answers
The correct equations for x = - 2 and x = 2 are,
⇒ x² - 4 = 0
⇒ 4x² = 16
We have to given that;
Find the equations which are true for x = - 2 and x = 2.
Now, We can simplify as;
⇒ x² - 4 = 0
⇒ x² = 4
⇒ x = ± 2
⇒ x² = - 4
⇒ x = ±2i
⇒ 3x² + 12 = 0
⇒ x² + 4 = 0
⇒ x = ±2i
⇒ 4x² = 16
⇒ x² = 4
⇒ x = ±2
⇒ 2 (x - 2)² = 0
⇒ (x - 2)² = 0
⇒ x = 2, 2
Thus, The correct equations for x = - 2 and x = 2 are,
⇒ x² - 4 = 0
⇒ 4x² = 16
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Suppose each license plate in a certain state has three digits followed by three letters. The digits 4 and 5 are not used. So, there are 26 letters and 8 digits that
are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format?
license plates
X
Answers
The requried, there are 8998912 possible license plates that can be generated using this format.
There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used. Therefore, there are 8 choices for each of the three digits, giving us 8 x 8 x 8 = 512 possible combinations for the digits.
Similarly, there are 26 letters that can be used for each of the three letters on the license plate. Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.
Total number of license plates = number of choices for the digits x number of choices for the letters
= 512 x 17576
= 8998912
Therefore, there are 8998912 possible license plates that can be generated using this format.
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Erik is growing vegetables in a square garden in his backyard. Each side of the vegetable garden is 6 feet long. He is also growing herbs in a rectangular garden that is 4 feet long and 3 feet wide. How many square feet larger is the vegetable garden than the herb garden?
Answers
the vegetable garden is 24 square feet larger than the herb garden. The area of the square vegetable garden is equal to the length of one side squared.
what is larger than ?
"larger than" is a comparative term used to describe a situation where one thing has a greater size, quantity, value, or magnitude than another thing. It is used to indicate a comparison between two or more objects or quantities.
In the given question,
The area of the square vegetable garden is equal to the length of one side squared. Each side of the square garden is 6 feet long, so the area of the vegetable garden is:
6 feet × 6 feet = 36 square feet
The area of the rectangular herb garden is equal to its length multiplied by its width. The length of the herb garden is 4 feet and the width is 3 feet, so the area of the herb garden is:
4 feet × 3 feet = 12 square feet
To find the difference in area between the two gardens, we subtract the area of the herb garden from the area of the vegetable garden:
36 square feet - 12 square feet = 24 square feet
Therefore, the vegetable garden is 24 square feet larger than the herb garden.
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Answers
The area of the composite figure is 84.85 square units
How to find the area of the composite figureThe area of the composite figure is solved by breaking it up and adding together
To find the area of a semicircle of diameter 8, we first need to find the radius of the semicircle, which is half of the diameter:
radius = diameter / 2 = 8 / 2 = 4
area of semicircle = (1/2) * pi * radius^2
= (1/2) * pi * 4^2
= 8 pi
Now, let's find the area of the parallelogram. The area of a parallelogram is given by the formula:
area of parallelogram = base * height
In this case, the base is 10 and the height is 6, so we have:
area of parallelogram = 10 * 6
= 60
total area = area of semicircle + area of parallelogram
= 8 pi + 60
= 60 + 8 pi (in exact form) or approximately 84.85 (rounded to two decimal places)
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